Async/await is a nice-to-have syntax sugar, but not required to write asynchronous code, and considering the substantial under-the-hood complexity I'm not sure if async/await is a good thing overall, especially in a low level systems programming language like Zig (or FWIW, also Rust and C++).
Arguably, promises are an important concept in JS because it's a convenient and composable method to let code complete "in the background" without proper multithreading, but promises work just fine without the async/await code transformation magic (which even in JS is just the cherry on the top, but not a must-have feature).
> sanitary minimal API for a stack object + state machine + set/longjmp builtin primitives
Traditional async/await doesn't use most of that but instead relies on the compiler to transform sequential 'async code' into a switch-case state machine. What you want sounds more like green threads / fibers with stack switching. This isn't portable to some platforms where the call stack isn't accessible (like WASM). But as I wrote above, I think that lowest layer should simply be 'stdlib functions with completion callbacks'. Those low level functions can then be wrapped into all sorts of asynchronous/multithreading runtimes.
FWIW, I think a stack-switching fiber runtime should be possible in Zig without special language primitives, because Zig has inline assembly: https://ziglang.org/documentation/master/#Assembly